https://orcid.org/0000-0002-2111-7596
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Abstract
For each integer b ≥ 3 and every x ≥ 1, let 
b,0(x) be the set of positive integers n ≤ x which are divisible by the product of their nonzero base b digits. We prove bounds of the form xρb,0+o(1) < #
b,0(x) < xηb,0+o(1), as x → +∞, where ρb,0 and ηb,0 are constants in ]0, 1[ depending only on b. In particular, we show that x0.526 < #
10,0(x) < x0.787, for all sufficiently large x. This improves the bounds x0.495 < #
10,0(x) < x0.901, which were proved by De Koninck and Luca.
Mathematics Subject Classification (2010):
Key words: